PHILOSOPHICAL ENQUIRIES; (continued 2)

It then occurred to him, that, if the Earth was supposed to revolve every day round its axis, from west to east, all the heavenly bodies would appear to revolve, in a contrary direction, from east to west. The diurnal revolution of the heavens, upon this hypothesis, might be only apparent; the firmament, which has no other sensible motion, might be perfectly at rest; while the Sun, the Moon, and the Five Planets, might have no other movement beside that eastward revolution, which is peculiar to themselves. That, by supposing the Earth to revolve with the Planets, round the Sun, in an orbit, which comprehended within it the orbits of Venus and Mercury, but was comprehended within those of Mars, Jupiter, and Saturn, he could, without the embarrassment of Epicycles, connect together the apparent annual revolutions of the Sun, and the direct, retrograde, and stationary appearances of the Planets: that while the Earth really revolved round the Sun on one side of the heavens, the Sun would appear to revolve round the Earth on the other; that while she really advanced in her annual course, he would appear to advance eastward in that movement which is peculiar to himself. That, by supposing the axis of the Earth to be always parallel to itself, not to be quite perpendicular, but somewhat inclined to the plane of her orbit, and consequently to present to the Sun, the one pole when on the one side of him, and the other when on the other, he would account for the obliquity of the Ecliptic; the Sun’s seemingly alternate progression from north to south, and from south to north, the consequent change of the seasons, and different lengths of the days and nights in the different seasons.

If this new hypothesis thus connected together all these appearances as happily as that of Ptolemy, there were others which it connected together much better. The three superior Planets, when nearly in conjunction with the Sun, appear always at the greatest distance from the Earth, are smallest, and least sensible to the eye, and seem to revolve forward in their direct motion with the greatest rapidity. On the contrary, when in opposition to the Sun, that is, when in their meridian about midnight, they appear nearest the Earth, are largest, and most sensible to the eye, and seem to revolve backwards in their retrograde motion. To explain these appearances, the system of Ptolemy supposed each of these Planets to be at the upper part of their several Epicycles, in the one case; and at the lower, in the other. But it afforded no satisfactory principle of connection, which could lead the mind easily to conceive how the Epicycles of those Planets, whose spheres were so distant from the sphere of the Sun, should thus, if one may say so, keep time to his motion. The system of Copernicus afforded this easily, and like a more simple machine, without the assistance of Epicycles, connected together, by fewer movements, the complex appearances of the heavens. When the superior Planets appear nearly in conjunction with the Sun, they are then in the side of their orbits, which is almost opposite to, and most distant from the Earth, and therefore appear smallest, and least sensible to the eye. But, as they then revolve in a direction which is almost contrary to that of the Earth, they appear to advance forward with double velocity; as a ship, that sails in a contrary direction to another, appears from that other, to sail both with its own velocity, and the velocity of that from which it is seen. On the contrary, when those Planets are in opposition to the Sun, they are on the same side of the Sun with the Earth, are nearest it, most sensible to the eye, and revolve in the same direction with it; but, as their revolutions round the Sun are slower than that of the Earth, they are necessarily left behind by it, and therefore seem to revolve backwards; as a ship which sails slower than another, though it sails in the same direction, appears from that other to sail backwards. After the same manner, by the same annual revolution of the Earth, he connected together the direct and retrograde motions of the two inferior Planets, as well as the stationary appearances of all the Five.

There are some other particular phenomena of the two inferior Planets, which correspond still better to this system, and still worse to that of Ptolemy. Venus and Mercury seem to attend constantly upon the motion of the Sun, appearing, sometimes on the one side, and sometimes on the other, of that great luminary; Mercury being almost always buried in his rays, and Venus never receding above forty-eight degrees from him, contrary to what is observed in the other three Planets, which are often seen in the opposite side of the heavens, at the greatest possible distance from the Sun. The system of Ptolemy accounted for this, by supposing that the centres of the Epicycles of these two Planets were always in the same line with those of the Sun and the Earth; that they appeared therefore in conjunction with the Sun, when either in the upper or lower part of their Epicycles, and at the greatest distance from him, when in the sides of them. It assigned, however, no reason why the Epicycles of these two Planets should observe so different a rule from that which takes place in those of the other three, nor for the enormous Epicycle of Venus, whose sides must have been forty-eight degrees distant from the Sun, while its centre was in conjunction with him, and whose diameter must have covered more than a quadrant of the Great Circle. But how easily all these appearances coincide with the hypothesis, which represents those two inferior Planets revolving round the Sun in orbits comprehended within the orbit of the Earth, is too obvious to require an explanation.

Thus far did this new account of things render the appearances of the heavens more completely coherent than had been done by any of the former systems. It did this, too, by a more simple and intelligible, as well as more beautiful machinery. It represented the Sun, the great enlightener of the universe, whose body was alone larger than all the Planets taken together, as established immovable in the centre, shedding light and heat on all the worlds that circulated around him in one uniform direction, but in longer or shorter periods, according to their different distances. It took away the diurnal revolution of the firmament, whose rapidity, upon the old hypothesis, was beyond what even thought could conceive. It not only delivered the imagination from the embarrassment of Epicycles, but from the difficulty of conceiving these two opposite motions going on at the same time, which the system of Ptolemy and Aristotle bestowed upon all the Planets; I mean, their diurnal westward, and periodical eastward revolutions. The Earth’s revolution round its own axis took away the necessity for supposing the first, and the second was easily conceived when by itself. The Five Planets, which seem, upon all other systems, to be objects of a species by themselves, unlike to every thing to which the imagination has been accustomed, when supposed to revolve along with the Earth round the Sun, were naturally apprehended to be objects of the same kind with the Earth, habitable, opaque, and enlightened only by the rays of the Sun. And thus this hypothesis, by classing them in the same species of things, with an object that is of all others the most familiar to us, took off that wonder and that uncertainty which the strangeness and singularity of their appearance had excited; and thus far, too, better answered the great end of Philosophy.

Neither did the beauty and simplicity of this system alone recommend it to the imagination; the novelty and unexpectedness of that view of nature, which it opened to the fancy, excited more wonder and surprise than the strangest of those appearances, which it had been invented to render natural and familiar, and these sentiments still more endeared it. For, though it is the end of Philosophy, to allay that wonder, which either the unusual or seemingly disjointed appearances of nature excite, yet she never triumphs so much, as when, in order to connect together a few, in themselves, perhaps, inconsiderable objects, she has, if I may say so, created another constitution of things, more natural, indeed, and such as the imagination can more easily attend to, but more new, more contrary to common opinion and expectation, than any of those appearances themselves. As, in the instance before us, in order to connect together some seeming irregularities in the motions of the Planets, the most inconsiderable objects in the heavens, and of which the greater part of mankind have no occasion to take any notice during the whole course of their lives, she has, to talk in the hyperbolical language of Tycho Brahe, moved the Earth from its foundations, stopped the revolution of the Firmament, made the Sun stand still, and subverted the whole order of the Universe.

Such were the advantages of this new hypothesis, as they appeared to its author, when he first invented it. But, though that love of paradox, so natural to the learned, and that pleasure, which they are so apt to take in exciting, by the novelties of their supposed discoveries, the amazement of mankind, may, notwithstanding what one of his disciples tells us to the contrary, have had its weight in prompting Copernicus to adopt this system; yet, when he had completed his Treatise of Revolutions, and began coolly to consider what a strange doctrine he was about to offer to the world, he so much dreaded the prejudice of mankind against it, that, by a species of continence, of all others the most difficult to a philosopher, he detained it in his closet for thirty years together. At last, in the extremity of old age, he allowed it to be extorted from him, but he died as soon as it was printed, and before it was published to the world.

When it appeared in the world, it was almost universally disapproved of, by the learned as well as by the ignorant. The natural prejudices of sense, confirmed by education, prevailed too much with both, to allow them to give it a fair examination. A few disciples only, whom he himself had instructed in his doctrine, received it with esteem and admiration. One of them, Reinholdus, formed, upon this hypothesis, larger and more accurate astronomical tables, than what accompanied the Treatise of Revolutions, in which Copernicus had been guilty of some errors in calculation. It soon appeared, that these Prutenic Tables, as they were called, corresponded more exactly with the heavens, than the Tables of Alphonsus. This ought naturally to have formed a prejudice in favour of the diligence and accuracy of Copernicus in observing the heavens. But it ought to have formed none in favour of his hypothesis; since the same observations, and the result of the same calculations, might have been accommodated to the system of Ptolemy, without making any greater alteration in that system than what Ptolemy had foreseen, and had even foretold should be made. It formed, however, a prejudice in favour of both, and the learned began to examine, with some attention, an hypothesis which afforded the easiest methods of calculation, and upon which the most exact predictions had been made. The superior degree of coherence, which it bestowed upon the celestial appearances, the simplicity and uniformity which it introduced into the real directions and velocities of the Planets, soon disposed many astronomers, first to favour, and at last to embrace a system, which thus connected together so happily, the most disjointed of those objects that chiefly occupied their thoughts. Nor can any thing more evidently demonstrate, how easily the learned give up the evidence of their senses to preserve the coherence of the ideas of their imagination, than the readiness with which this, the most violent paradox in all philosophy, was adopted by many ingenious astronomers, notwithstanding its inconsistency with every system of physics then known in the world, and notwithstanding the great number of other more real objections, to which, as Copernicus left it, this account of things was most justly exposed.

It was adopted, however, nor can this be wondered at, by astronomers only. The learned in all other sciences, continued to regard it with the same contempt as the vulgar. Even astronomers were divided about its merit; and many of them rejected a doctrine, which not only contradicted the established system of Natural Philosophy, but which, considered astronomically only, seemed, to them, to labour under several difficulties.

Some of the objections against the motion of the Earth, that were drawn from the prejudices of sense, the patrons of this system, indeed, easily enough got over. They represented, that the Earth might really be in motion, though, to its inhabitants, it seemed to be at rest; and that the Sun and Fixed Stars might really be at rest, though from the Earth they seemed to be in motion; in the same manner as a ship, which sails through a smooth sea, seems to those who are in it, to be at rest, though really in motion; while the objects which she passes along, seem to be in motion, though really at rest.

But there were some other objections, which, though grounded upon the same natural prejudices, they found it more difficult to get over. The earth had always presented itself to the senses, not only as at rest, but as inert, ponderous, and even averse to motion. The imagination had always been accustomed to conceive it as such, and suffered the greatest violence, when obliged to pursue, and attend it, in that rapid motion which the system of Copernicus bestowed upon it. To enforce their objection, the adversaries of this hypothesis were at pains to calculate the extreme rapidity of this motion. They represented, that the circumference of the Earth had been computed to be above twenty-thousand miles: if the Earth, therefore, was supposed to revolve every day round its axis, every point of it near the equator would pass over above twenty-three thousand miles in a day; and consequently, near a thousand miles in an hour, and about sixteen miles in a minute; a motion more rapid than that of a cannon ball, or even than the swifter progress of sound. The rapidity of its periodical revolution was yet more violent than that of its diurnal rotation. How, therefore, could the imagination ever conceive so ponderous a body to be naturally endowed with so dreadful a movement? The Peripatetic Philosophy, the only philosophy then known in the world, still further confirmed this prejudice. That philosophy, by a very natural, though, perhaps, groundless distinction, divided all motion into Natural and Violent. Natural motion was that which flowed from an innate tendency in the body, as when a stone fell downwards: Violent motion, that which arose from external force, and which was, in some measure, contrary to the natural tendency of the body, as when a stone was thrown upwards, or horizontally. No violent motion could be lasting; for, being constantly weakened by the natural tendency of the body, it would soon be destroyed. The natural motion of the Earth, as was evident in all its parts, was downwards, in a straight line to the centre; as that of fire and air was upwards, in a straight line from the centre. It was the heavens only that revolved naturally in a circle. Neither, therefore, the supposed revolution of the Earth round its own centre, nor that round the Sun, could be natural motions; they must therefore be violent, and consequently could be of no long continuance. It was in vain that Copernicus replied, that gravity was, probably, nothing else besides a tendency in the different parts of the same Planet, to unite themselves to one another; that this tendency took place, probably, in the parts of the other Planets, as well as in those of the Earth; that it could very well be united with a circular motion; that it might be equally natural to the whole body of the Planet, and to every part of it; that his adversaries themselves allowed, that a circular motion was natural to the heavens, whose diurnal revolution was infinitely more rapid than even that motion which he had bestowed upon the Earth; that though a like motion was natural to the Earth, it would still appear to be at rest to its inhabitants, and all the parts of it to tend in a straight line to the centre, in the same manner as at present. But this answer, how satisfactory soever it may appear to be now, neither did nor could appear to be satisfactory then. By admitting the distinction betwixt natural and violent motions, it was founded upon the same ignorance of mechanical principles with the objection. The systems of Aristotle and Hipparchus supposed, indeed, the diurnal motion of the heavenly bodies to be infinitely more rapid than even that dreadful movement which Copernicus bestowed upon the Earth. But they supposed, at the same time, that those bodies were objects of a quite different species, from any we are acquainted with, near the surface of the Earth, and to which, therefore, it was less difficult to conceive that any sort of motion might be natural. Those objects, besides, had never presented themselves to the senses, as moving otherwise, or with less rapidity, than these systems represented them. The imagination, therefore, could feel no difficulty in following a representation which the senses had rendered quite familiar to it. But when the Planets came to be regarded as so many Earths, the case was quite altered. The imagination had been accustomed to conceive such objects as tending rather to rest than motion; and this idea of their natural inertness, encumbered, if one may say so, and clogged its flight whenever it endeavoured to pursue them in their periodical courses, and to conceive them as continually rushing through the celestial spaces, with such violent and unremitting rapidity.

Nor were the first followers of Copernicus more fortunate in their answers to some other objections, which were founded indeed in the same ignorance of the laws of motion, but which, at the same time, were necessarily connected with that way of conceiving things, which then prevailed universally in the learned world.

If the earth, it was said, revolved so rapidly from west to east, a perpetual wind would set in from east to west, more violent than what blows in the greatest hurricanes; a stone, thrown westwards would fly to a much greater distance than one thrown with the same force eastwards; as what moved in a direction, contrary to the motion of the Earth, would necessarily pass over a greater portion of its surface, than what, with the same velocity, moved along with it. A ball, it was said, dropped from the mast of a ship under sail, does not fall precisely at the foot of the mast, but behind it; and in the same manner, a stone dropped from a high tower would not, upon the supposition of the Earth’s motion, fall precisely at the bottom of the tower, but west of it, the Earth being, in the mean time, carried away eastward from below it. It is amusing to observe, by what, subtile and metaphysical evasions the followers of Copernicus endeavoured to elude this objection, which before the doctrine of the Composition of Motion had been explained by Galileo, was altogether unanswerable. They allowed, that a ball dropped from the mast of a ship under sail would not fall at the foot of the mast, but behind it; because the ball, they said, was no part of the ship, and because the motion of the ship was natural neither to itself nor to the ball. But the stone was a part of the earth, and the diurnal and annual revolutions of the Earth were natural to the whole, and to every part of it, and therefore to the stone. The stone, therefore, having naturally the same motion with the Earth, fell precisely at the bottom of the tower. But this answer could not satisfy the imagination, which still found it difficult to conceive how these motions could be natural to the earth; or how a body, which had always presented itself to the senses as inert, ponderous, and averse to motion, should naturally be continually wheeling about both its own axis and the Sun, with such violent rapidity. It was, besides, argued by Tycho Brahe, upon the principles of the same philosophy which had afforded both the objection and the answer, that even upon the supposition, that any such motion was natural to the whole body of the Earth, yet the stone, which was separated from it, could no longer be actuated by that motion. The limb, which is cut off from an animal, loses those animal motions which were natural to the whole. The branch, which is cut off from the trunk, loses that vegetative motion which is natural to the whole tree. Even the metals, minerals, and stones, which were dug out from the bosom of the Earth, lose those motions which occasioned their production and increase, and which were natural to them in their original state. Though the diurnal and annual motion of the Earth, therefore, had been natural to them while they were contained in its bosom, it could no longer be so when they were separated from it.

Tycho Brahe, the great restorer of the science of the heavens, who had spent his life, and wasted his fortune upon the advancement of Astronomy, whose observations were both more numerous and more accurate than those of all the astronomers who had gone before him, was himself so much affected by the force of this objection, that, though he had never mentioned the system of Copernicus without some note of high admiration he had conceived for its author, he could never himself be induced to embrace it; yet all his astronomical observations tended to confirm it. They demonstrated, that Venus and Mercury were sometimes above, and sometimes below the Sun; and that, consequently, the Sun, and not the Earth, was the centre of their periodical revolutions. They showed, that Mars, when in his meridian at midnight, was nearer to the Earth than the Earth is to the Sun; though, when in conjunction with the Sun, he was much more remote from the Earth than that luminary; a discovery which was absolutely inconsistent with the system of Ptolemy, which proved, that the Sun, and not the Earth, was the centre of the periodical revolutions of Mars, as well as of Venus and Mercury; and which demonstrated that the Earth was placed betwixt the orbits of Mars and Venus. They made the same thing probable with regard to Jupiter and Saturn; that they, too, revolved round the Sun; and that, therefore, the Sun, if not the centre of the universe, was at least, that of the planetary system. They proved that Comets were superior to the Moon, and moved through the heavens in all possible directions; an observation incompatible with the Solid Spheres of Aristotle and Purbach, and which, therefore, overturned the physical part, at least, of the established systems of Astronomy.

All these observations, joined to his aversion to the system, and perhaps, notwithstanding the generosity of his character, some little jealousy for the fame of Copernicus, suggested to Tycho the idea of a new hypothesis, in which the Earth continued to be, as in the old account, the immovable centre of the universe, round which the firmament revolved every day from east to west, and, by some secret virtue, carried the Sun, the Moon, and the Five Planets along with it, notwithstanding their immense distance, and notwithstanding that there was nothing betwixt it and them but the most fluid ether. But, although all these seven bodies thus obeyed the diurnal revolution of the Firmament, they had each of them, as in the old system, too, a contrary periodical eastward revolution of their own, which made them appear to be every day, more or less, left behind by the Firmament. The Sun was the centre of the periodical revolutions of the Five Planets; the Earth, that of the Sun and Moon. The Five Planets followed the Sun in his periodical revolution round the Earth, as they did the Firmament in its diurnal rotation. The three superior Planets comprehended the Earth within the orbit in which they revolved round the Sun, and had each of them an Epicycle to connect together, in the same manner as in the system of Ptolemy, their direct, retrograde, and stationary appearances. As, notwithstanding their immense distance, they followed the Sun in his periodical revolution round the Earth, keeping always at an equal distance from him, they were necessarily brought much nearer to the Earth when in opposition to the Sun, than than when in conjunction with him. Mars, the nearest of them, when in his meridian at midnight, came within the orbit which the Sun described round the Earth, and consequently was then nearer to the Earth than the Earth was to the Sun. The appearances of the two inferior Planets were explained, in the same manner, as in the system of Copernicus, and consequently required no Epicycle to connect them. The circles in which the Five Planets performed their periodical revolutions round the Sun, as well as those in which the Sun and Moon performed theirs round the Earth, were, as both in the old and new hypothesis, Eccentric Circles, to connect together their differently accelerated and retarded motions.

Such was the system of Tycho Brahe, compounded, as is evident, out of these of Ptolemy and Copernicus; happier than that of Ptolemy, in the account which it gives of the motions of the two inferior Planets; more complex, by supposing the different revolutions of all the Five to be performed round two different centres; the diurnal round the Earth, the periodical round the Sun, but, in every respect, more complex and more incoherent than that of Copernicus. Such, however, was the difficulty that mankind felt in conceiving the motion of the Earth, that it long balanced the reputation of that otherwise more beautiful system. It may be said, that those who considered the heavens only, favoured the system of Copernicus, which connected so happily all the appearances which presented themselves there; but that those who looked upon the Earth, adopted the account of Tycho Brahe, which, leaving it at rest in the centre of the universe, did less violence to the usual habits of the imagination. The learned were, indeed, sensible of the intricacy, and of the many incoherences of that system; that it gave no account why the Sun, Moon, and Five Planets, should follow the revolution of the Firmament; or why the Five Planets, notwithstanding the immense distance of the three superior ones, should obey the periodical motion of the Sun; or why the Earth, though placed between the orbits of Mars and Venus, should remain immovable in the centre of the Firmament, and constantly resist the influence of whatever it was, which carried bodies that were so much larger than itself, and that were placed on all sides of it, periodically round the Sun. Tycho Brahe died before he had fully explained his system. His great and merited renown disposed many of the learned to believe, that, had his life been longer, he would have connected together many of these incoherences, and knew methods of adapting his system to some other appearances, with which none of his followers could connect it.

The objection to the system of Copernicus, which was drawn from the nature of motion, and that was most insisted on by Tycho Brahe, was at last fully answered by Galileo; not, however, till about thirty years after the death of Tycho, and about a hundred after that of Copernicus. It was then that Galileo, by explaining the nature of the composition of motion, by showing, both from reason and experience, that a ball dropped from the mast of a ship under sail would fall precisely at the foot of the mast, and by rendering this doctrine, from a great number of other instances, quite familiar to the imagination, took off, perhaps, the principal objection which had been made to this hypothesis of the astronomers.

Several other astronomical difficulties, which encumbered this account of things, were removed by the same philosopher. Copernicus, after altering the centre of the world, and making the Earth, and all the Planets revolve round the Sun, was obliged to leave the Moon to revolve round the Earth as before. But no example of any such secondary Planet having then been discovered in the heavens, there seemed still to be this irregularity remaining in the system. Galileo, who first applied telescopes to Astronomy, discovered, by their assistance, the Satellites of Jupiter, which, revolving round that Planet, at the same time that they were carried along with it in its revolution, round either the Earth, or the Sun, made it seem less contrary to the analogy of nature, that the Moon should both revolve round the Earth, and accompany her in her revolution round the Sun.

It had been objected to Copernicus, that, if Venus and Mercury revolved round the Sun in an orbit comprehended within the orbit of the Earth, they would show all the same phases with the Moon; present, sometimes their darkened, and sometimes their enlightened sides to the Earth, and sometimes part of the one, and part of the other. He answered, that they undoubtedly did all this; but that their smallness and distance hindered us from perceiving it. This very bold assertion of Copernicus was confirmed by Galileo. His telescopes rendered the phases of Venus quite sensible, and thus demonstrated, more evidently than had been done, even by the observations of Tycho Brahe, the revolutions of these two Planets round the Sun, as well as so far destroyed the system of Ptolemy.

The mountains and seas, which, by the help of the same instrument, he discovered, or imagined he had discovered in the Moon, rendering that Planet, in every respect, similar to the Earth, made it seem less contrary to the analogy of nature, that, as the Moon revolved round the Earth, the Earth should revolve round the Sun.

The spots which, in the same manner, he discovered in the Sun, demonstrating, by their motion, the revolution of the Sun round his axis, made it seem less improbable that the Earth, a body so much smaller than the Sun, should likewise revolve round her axis in the same manner.

Succeeding telescopical observations, discovered, in each of the Five Planets, spots not unlike those which Galileo had observed in the Moon, and thereby seemed to demonstrate what Copernicus had only conjectured, that the Planets were naturally opaque, enlightened only by the rays of the Sun, habitable, diversified by seas and mountains, and, in every respect, bodies of the same kind with the earth; and thus added one other probability to this system. By discovering, too, that each of the Planets revolved round its own axis, at the same time that it was carried round either the Earth or the Sun, they made it seem quite agreeable to the analogy of nature, that the Earth, which, in every other respect, resembled the Planets, should, like them too, revolve round its own axis, and at the same time perform its periodical motion round the Sun.

While, in Italy, the unfortunate Galileo was adding so many probabilities to the system of Copernicus, there was another philosopher employing himself in Germany, to ascertain, correct, and improve it; Kepler, with great genius, but without the taste, or the order and method of Galileo, possessed, like all his other countrymen, the most laborious industry, joined to that passion for discovering proportions and resemblances betwixt the different parts of nature, which, though common to all philosophers, seems, in him, to have been excessive. He had been instructed, by Mæstlinus, in the system of Copernicus; and his first curiosity was, as he tells us, to find out, why the Planets, the Earth being counted for one, were Six in number; why they were placed at such irregular distances from the Sun; and whether there was any uniform proportion betwixt their several distances, and the times employed in their periodical revolutions. Till some reason, or proportion of this kind, could be discovered, the system did not appear to him to be completely coherent. He endeavoured, first, to find it in the proportions of numbers, and plain figures; afterwards, in those of the regular solids; and, last of all, in those of the musical divisions of the Octave. Whatever was the science which Kepler was studying, he seems constantly to have pleased himself with finding some analogy betwixt it and the system of the universe; and thus, arithmetic and music, plane and solid geometry, came all of them by turns to illustrate the doctrine of the Sphere, in the explaining of which he was, by his profession, principally employed. Tycho Brahe, to whom he had presented one of his books, though he could not but disapprove of his system, was pleased, however, with his genius, and with his indefatigable diligence in making the most laborious calculations. That generous and magnificent Dane invited the obscure and indigent Kepler to come and live with him, and communicated to him, as soon as he arrived, his observations upon Mars, in the arranging and methodizing of which his disciples were at that time employed. Kepler, upon comparing them with one another, found, that the orbit of Mars was not a perfect circle; that one of its diameters was somewhat longer than the other; and that it approached to an oval, or an ellipse, which had the Sun placed in one of its foci. He found, too, that the motion of the Planet was not equable; that it was swiftest when nearest the Sun, and slowest when furthest from him; and that its velocity gradually increased, or diminished, according as it approached or receded from him. The observations of the same astronomer discovered to him, though not so evidently, that the same things were true of all the other Planets; that their orbits were elliptical, and that their motions were swiftest when nearest the Sun, and slowest when furthest from him. They showed the same things, too, of the Sun, if supposed to revolve round the Earth; and consequently of the Earth, if it also was supposed to revolve round the Sun.

That the motions of all the heavenly bodies were perfectly circular, had been the fundamental idea upon which every astronomical hypothesis, except the irregular one of the Stoics, had been built. A circle, as the degree of its curvature is every where the same, is of all curve lines the simplest and the most easily conceived. Since it was evident, therefore, that the heavenly bodies did not move in straight lines, the indolent imagination found, that it could most easily attend to their motions if they were supposed to revolve in perfect circles. It had, upon this account, determined that a circular motion was the most perfect of all motions, and that none but the most perfect motion could be worthy of such beautiful and divine objects; and it had upon this account, so often, in vain, endeavoured to adjust to the appearances, so many different systems, which all supposed them to revolve in this perfect manner.

The equality of their motions was another fundamental idea, which, in the same manner, and for the same reason, was supposed by all the founders of astronomical systems. For an equal motion can be more easily attended to, than one that is continually either accelerated or retarded. All inconsistency, therefore, was declared to be unworthy those bodies which revolved in the celestial regions, and to be fit only for inferior and sublunary things. The calculations of Kepler overturned, with regard to the Planets, both these natural prejudices of the imagination; destroyed their circular orbits; and introduced into their real motions, such an equality as no equalizing circle would remedy. It was, however, to render their motion perfectly equable, without even the assistance of a equalizing circle, that Copernicus, as he himself assures us, had originally invented his system. Since the calculations of Kepler, therefore, overturned what Copernicus had principally in view in establishing his system, we cannot wonder that they should at first seem rather to embarrass than improve it.

It is true, by these elliptical orbits and unequal motions, Kepler disengaged the system from the embarrassment of those small Epicycles, which Copernicus, in order to connect the seemingly accelerated and retarded movements of the Planets, with their supposed real equality, had been obliged to leave in it. For it is remarkable, that though Copernicus had delivered the orbits of the Planets from the enormous Epicycles of Hipparchus, that though in this consisted the great superiority of his system above that of the ancient astronomers, he was yet obliged, himself, to abandon, in some measure, this advantage, and to make use of some small Epicycles, to join together those seeming irregularities. His Epicycles indeed, like the irregularities for whose sake they were introduced, were but small ones, and the imaginations of his first followers seem, accordingly, either to have slurred them over altogether, or scarcely to have observed them. Neither Galileo, nor Gassendi, the two most eloquent of his defenders, take any notice of them. Nor does it seem to have been generally attended to, that there was any such thing as Epicycles in the system of Copernicus, till Kepler, in order to vindicate his own elliptical orbits, insisted, that even, according to Copernicus, the body of the Planet was to be found but at two different places in the circumference of that circle which the centre of its Epicycle described.

It is true, too, that an ellipse is, of all curve lines after a circle, the simplest and most easily conceived; and it is true, besides all this, that, while Kepler took from the motion of the Planets the easiest of all proportions, that of equality, he did not leave them absolutely without one, but ascertained the rule by which their velocities continually varied; for a genius so fond of analogies, when he had taken away one, would be sure to substitute another in its room. Notwithstanding all this, notwithstanding that his system was better supported by observations than any system had ever been before, yet, such was the attachment to the equal motions and circular orbits of the Planets, that it seems, for some time, to have been in general but little attended to by the learned, to have been altogether neglected by philosophers, and not much regarded even by astronomers.

Gassendi, who began to figure in the world about the latter days of Kepler, and who was himself no mean astronomer, seems indeed to have conceived a good deal of esteem for his diligence and accuracy in accommodating the observations of Tycho Brahe to the system of Copernicus. But Gassendi appears to have had no comprehension of the importance of those alterations which Kepler had made in that system, as is evident from his scarcely ever mentioning them in the whole course of his voluminous writings upon Astronomy. Des Cartes, the contemporary and rival of Gassendi, seems to have paid no attention to them at all, but to have built his Theory of the Heavens, without any regard to them. Even those astronomers, whom a serious attention had convinced of the justness of his corrections, were still so enamoured with the circular orbits and equal motion, that they endeavoured to compound his system with those ancient but natural prejudices. Thus, Ward endeavoured to show that, though the Planets moved in elliptical orbits, which had the Sun in one of their foci, and though their velocities in the elliptical line were continually varying, yet, if a ray was supposed to be extended from the centre of any one of them to the other focus, and to be carried along by the periodical motion of the Planet, it would make equal angles in equal times, and consequently cut off equal portions of the circle of which that other focus was the centre. To one, therefore, placed in that focus, the motion of the Planet would appear to be perfectly circular and perfectly equable, in the same manner as in the Equalizing Circles of Ptolemy and Hipparchus. Thus Bouillaud, who censured this hypothesis of Ward, invented another of the same kind, infinitely more whimsical and capricious. The Planets, according to that astronomer, always revolve in circles; for that being the most perfect figure, it is impossible they should revolve in any other. No one of them, however, continues to move in any one circle, but is perpetually passing from one to another, through an infinite number of circles, in the course of each revolution; for an ellipse, said he, is an oblique section of a cone, and in a cone, betwixt the two vortices of the ellipse there is an infinite number of circles, out of the infinitely small portions of which the elliptical line is compounded. The Planet, therefore which moves in this line, is, in every point of it, moving in an infinitely small portion of a certain circle. The motion of each Planet, too, according to him, was necessarily, for the same reason, perfectly equable. An equable motion being the most perfect of all motions. It was not, however, in the elliptical line, that it was equable, but in any one of the circles that were parallel to the base of that cone, by whose section this elliptical line had been formed: for, if a ray was extended from the Planet to any one of those circles, and carried along by its periodical motion, it would cut off equal portions of that circle in equal times; another most fantastical equalising circle, supported by no other foundation besides the frivolous connection between a cone and an ellipse, and recommended by nothing but the natural passion for circular orbits and equable motions. It may be regarded as the last effort of this passion, and may serve to show the force of that principle which could thus oblige this accurate observer, and great improver of the Theory of the Heavens, to adopt so strange an hypothesis. Such was the difficulty and hesitation with which the followers of Copernicus adopted the corrections of Kepler.

The rule, indeed, which Kepler ascertained for determining the gradual acceleration or retardation in the movement of the Planets, was intricate, and difficult to be comprehended; it could therefore but little facilitate the progress of the imagination in tracing those revolutions which were supposed to be conducted by it. According to that astronomer, if a straight line was drawn from the centre of each Planet to the Sun, and carried along by the periodical motion of the Planet, it would describe equal areas in equal times, though the Planet did not pass over equal spaces; and the same rule he found, took place nearly with regard to the Moon. The imagination, when acquainted with the law by which any motion is accelerated or retarded, can follow and attend to it more easily, than when at a loss, and, as it were, wandering in uncertainty with regard to the proportion which regulates its varieties; the discovery of this analogy therefore, no doubt, rendered the system of Kepler more agreeable to the natural taste of mankind: it, was, however, an analogy too difficult to be followed, or comprehended, to render it completely so.

Kepler, besides this, introduced another new analogy into the system, and first discovered, that there was one uniform relation observed betwixt the distances of the Planets from the Sun, and the times employed in their periodical motions. He found, that their periodical times were greater than in proportion to their distances, and less than in proportion to the squares of those distances; but, that they were nearly as the mean proportionals betwixt their distances and the squares of their distances; or, in other words, that the squares of their periodical times were nearly as the cubes of their distances; an analogy, which, though, like all others, it no doubt rendered the system somewhat more distinct and comprehensible, was, however, as well as the former, of too intricate a nature to facilitate very much the effort of the imagination in conceiving it.

The truth of both these analogies, intricate as they were, was at last fully established by the observations of Cassini. That astronomer first discovered, that the secondary Planets of Jupiter and Saturn revolved round their primary ones, according to the same laws which Kepler had observed in the revolutions of the primary ones round the Sun, and that of the Moon round the earth; that each of them described equal areas in equal times, and that the squares of their periodic times were as the cubes of their distances. When these two last abstruse analogies, which, when Kepler at first observed them, were but little regarded, had been thus found to take place in the revolutions of the Four Satellites of Jupiter, and in those of the Five of Saturn, they were now thought not only to confirm the doctrine of Kepler, but to add a new probability to the Copernican hypothesis. The observations of Cassini seem to establish it as a law of the system, that, when one body revolved round another, it described equal areas in equal times; and that, when several revolved round the same body, the squares of their periodic times were as the cubes of their distances. If the Earth and the Five Planets were supposed to revolve round the Sun, these laws, it was said, would take place universally. But if, according to the system of Ptolemy, the Sun, Moon, and Five Planets were supposed to revolve round the Earth, the periodical motions of the Sun and Moon, would, indeed, observe the first of these laws, would each of them describe equal areas in equal times; but they would not observe the second, the squares of their periodic times would not be as the cubes of their distances: and the revolutions of the Five Planets would observe neither the one law nor the other. Or if, according to the system of Tycho Brahe, the Five Planets were supposed to revolve round the Sun, while the Sun and Moon revolved round the Earth, the revolutions of the Five Planets round the Sun, would, indeed, observe both these laws; but those of the Sun and Moon round the Earth would observe only the first of them. The analogy of nature, therefore, could be preserved completely, according to no other system but that of Copernicus, which, upon that account, must be the true one. This argument is regarded by Voltaire, and the Cardinal of Polignac, as an irrefragable demonstration; even M‘Laurin, who was more capable of judging, nay, Newton himself, seems to mention it as one of the principal evidences for the truth of that hypothesis. Yet, an analogy of this kind, it would seem, far from a demonstration, could afford, at most, but the shadow of a probability.

It is true, that though Cassini supposed the Planets to revolve in an oblong curve, it was in a curve somewhat different from that of Kepler. In the ellipse, the sum of the two lines which are drawn from any one point in the circumference to the two foci, is always equal to that of those which are drawn from any other point in the circumference to the same foci. In the curve of Cassini, it is not the sum of the lines, but the rectangles which are contained under the lines, that are always equal. As this, however, was a proportion more difficult to be comprehended by astronomers than the other, the curve of Cassini has never had the vogue.

Nothing now embarrassed the system of Copernicus, but the difficulty which the imagination felt in conceiving bodies so immensely ponderous as the Earth and the other Planets revolving round the Sun with such incredible rapidity. It was in vain that Copernicus pretended, that, notwithstanding the prejudices of sense, this circular motion might be as natural to the Planets, as it is to a stone to fall to the ground. The imagination had been accustomed to conceive such objects as tending rather to rest than motion. This habitual idea of their natural inertness was incompatible with that of their natural motion. It was in vain that Kepler, in order to assist the fancy in connecting together this natural inertness with their astonishing velocities, talked of some vital and immaterial virtue, which was shed by the Sun into the surrounding spaces, which was whirled about with his revolution round his own axis, and which, taking hold of the Planets, forced them, in spite of their ponderousness and strong propensity to rest, thus to whirl about the centre of the system. The imagination had no hold of this immaterial virtue, and could form no determinate idea of what it consisted in. The imagination, indeed, felt a gap, or interval, betwixt the constant motion and the supposed inertness of the Planets, and had in this, as in all other cases, some general idea or apprehension that there must be a connecting chain of intermediate objects to link together these discordant qualities. Wherein this connecting chain consisted, it was, indeed, at a loss to conceive; nor did the doctrine of Kepler lend it any assistance in this respect. That doctrine, like almost all those of the philosophy in fashion during his time, bestowed a name upon this invisible chain, called it an immaterial virtue, but afforded no determinate idea of what was its nature.

Des Cartes was the first who attempted to ascertain, precisely, wherein this invisible chain consisted, and to afford the imagination a train of intermediate events, which, succeeding each other in an order that was of all others the most familiar to it, should unite those incoherent qualities, the rapid motion, and the natural inertness of the Planets. Des Cartes was the first who explained wherein consisted the real inertness of matter; that it was not in an aversion to motion, or in a propensity to rest, but in a power of continuing indifferently either at rest of in motion, and of resisting, with a certain force, whatever endeavoured to change its state from the one to the other. According to that ingenious and fanciful philosopher, the whole of infinite space was full of matter, for with him matter and extension were the same, and consequently there could be no void. This immensity of matter, he supposed to be divided into an infinite number of very small cubes; all of which, being whirled about upon their own centres, necessarily gave occasion to the production of two different elements. The first consisted of those angular parts, which, having been necessarily rubbed off, and grinded yet smaller by their mutual friction, constituted the most subtle and movable part of matter. The second consisted of those little globules that were formed by the rubbing off of the first. The interstices betwixt these globules of the second element was filled up by the particles of the first. But in the infinite collisions, which must occur in an infinite space filled with matter, and all in motion, it must necessarily happen that many of the globules of the second element should be broken and grinded down into the first. The quantity of the first element having been thus increased beyond what was sufficient to fill up the interstices of the second, it must, in many places, have been heaped up together, without any mixture of the second along with it. Such, according to Des Cartes, was the original division of matter. Upon this infinitude of matter thus divided, a certain quantity of motion was originally impressed by the Creator of all things, and the laws of motion were so adjusted as always to preserve the same quantity in it, without increase, and without diminution. Whatever motion was lost by one part of matter, was communicated to some other; and whatever was acquired by one part of matter, was derived from some other: and thus, through an eternal revolution, from rest to motion, and from motion to rest, in every part of the universe, the quantity of motion in the whole was always the same.

But, as there was no void, no one part of matter could be moved without thrusting some other out of its place, nor that without thrusting some other, and so on. To avoid, therefore, an infinite progress, he supposed that the matter which any body pushed before it, rolled immediately backwards, to supply the place of that matter which flowed in behind it; and as we may observe in the swimming of a fish, that the water which it pushes before it, immediately rolls backward, to supply the place of what flows in behind it, and thus forms a small circle or vortex round the body of the fish. It was, in the same manner, that the motion originally impressed by the Creator upon the infinitude of matter, necessarily produced in it an infinity of greater and smaller vortices, or circular streams: and the law of motion being so adjusted as always to preserve the same quantity of motion in the universe, those vortices either continued for ever, or by their dissolution gave birth to others of the same kind. There was, thus, at all times, an infinite number of greater and smaller vortices, or circular streams, revolving in the universe.

But, whatever moves in a circle, is constantly endeavouring to fly off from the centre of its revolution. For the natural motion of all bodies is in a straight line. All the particles of matter, therefore, in each of those greater vortices, were continually pressing from the centre to the circumference, with more or less force, according to the different degrees of their bulk and solidity. The larger and more solid globules of the second element forced themselves upwards to the circumference, while the smaller, more yielding, and more active particles of the first, which could flow, even through the interstices of the second, were forced downwards to the centre. They were forced downwards to the centre, notwithstanding their natural tendency was upwards to the circumference; for the same reason that a piece of wood, when plunged in water, is forced upwards to the surface, notwithstanding its natural tendency is downwards to the bottom; because its tendency downwards is less strong than that of the particles of water, which, therefore, if one may say so, press in before it, and thus force it upwards. But there being a greater quantity of the first element than what was necessary to fill up the interstices of the second, it was necessarily accumulated in the centre of each of these great circular streams, and formed there the fiery and active substance of the Sun. For, according to that philosopher, the Solar Systems were infinite in number, each Fixed Star being the centre of one: and he is among the first of the moderns, who thus took away the boundaries of the Universe; even Copernicus and Kepler, themselves, having confined it within, what they supposed, to be the vault of the Firmament.

The centre of each vortex being thus occupied by the most active and movable parts of matter, there was necessarily among them, a more violent agitation than in any other part of the vortex, and this violent agitation of the centre cherished and supported the movement of the whole. But, among the particles of the first element, which fill up the interstices of the second, there are many, which, from the pressure of the globules on all sides of them, necessarily receive an angular form, and thus constitute a third element of particles less fit for motion than those of the other two. As the particles, however, of this third element were formed in the interstices of the second, they are necessarily smaller than those of the second, and are, therefore, along with those of the first, urged down towards the centre, where, when a number of them happen to take hold of one another, they form such spots upon the surface of the accumulated particles of the first element, as are often discovered by telescopes upon the face of that Sun which enlightens and animates our particular system. Those spots are often broken and dispelled, by the violent agitation of the particles of the first element, as has hitherto happily been the case with those which have successively been formed upon the face of our Sun. Sometimes, however, they encrust the whole surface of that fire which is accumulated in the centre; and the communication betwixt the most active and the most inert parts of the vortex being thus interrupted, the rapidity of its motion immediately begins to languish, and can no longer defend it from being swallowed up and carried away by the superior violence of some other like circular stream; and in this manner, what was once a Sun, becomes a Planet. Thus, the time was, according to this system, when the Moon was a body of the same kind with the Sun, the fiery centre of a circular stream of ether, which flowed continually round her; but her face having been crusted over by a congeries of angular particles, the motion of this circular stream began to languish, and could no longer defend itself from being absorbed by the more violent vortex of the Earth, which was then, too, a Sun, and which chanced to be placed in its neighbourhood. The Moon, therefore, became a Planet, and revolved round the Earth. In process of time, the same fortune, which had thus befallen the Moon, befell also the Earth; its face was encrusted by a gross and inactive substance; the motion of its vortex began to languish, and it was absorbed by the greater vortex of the Sun: but though the vortex of the Earth had thus become languid, it still had force enough to occasion both the diurnal revolution of the Earth, and the monthly motion of the Moon. For a small circular stream may easily be conceived as flowing round the body of the Earth, at the same time that it is carried along by that great ocean of ether which is continually revolving round the Sun; in the same manner, as in a great whirlpool of water, one may often see several small whirlpools, which revolve round centres of their own, and at the same time are carried round the centre of the great one. Such was the cause of the original formation and consequent motions of the Planetary System. When a solid body is turned round its centre, those parts of it, which are nearest, and those which are remotest from the centre, complete their revolutions in one and the same time. But it is otherwise with the revolutions of a fluid; the parts of it which are nearest the centre complete their revolutions in a shorter time, than those which are remoter. The Planets, therefore, all floating, in that immense tide of ether which is continually setting in from west to east round the body of the Sun, complete their revolutions in a longer or a shorter time, according to their nearness or distance from him. There was, however, according to Des Cartes, no very exact proportion observed betwixt the times of their revolutions and their distances from the centre. For that nice analogy, which Kepler had discovered betwixt them, having not yet been confirmed by the observations of Cassini, was, as I before took notice, entirely disregarded by Des Cartes. According to him, too, their orbits might not be perfectly circular, but be longer the one way than the other, and thus approach to an Ellipse. Nor yet was it necessary to suppose, that they described this figure with geometrical accuracy, or even that they described always precisely the same figure. It rarely happens, that nature can be mathematically exact with regard to the figure of the objects she produces, upon account of the infinite combinations of impulses, which must conspire to the production of each of her effects. No two Planets, no two animals of the same kind, have exactly the same figure, nor is that of any one of them perfectly regular. It was in vain, therefore, that astronomers laboured to find that perfect constancy and regularity in the motions of the heavenly bodies, which is to be found in no other parts of nature. These motions, like all others, must either languish or be accelerated, according as the cause which produces them, the revolution of the vortex of the Sun, either languishes, or is accelerated; and there are innumerable events which may occasion either the one or the other of those changes.

It was thus, that Des Cartes endeavoured to render familiar to the imagination, the greatest difficulty in the Copernican system, the rapid motion of the enormous bodies of the Planets. When the fancy had thus been taught to conceive them as floating in an immense ocean of ether, it was quite agreeable to its usual habits to conceive, that they should follow the stream of this ocean, how rapid soever. This was an order of succession to which it had been long accustomed, and with which it was, therefore, quite familiar. This account, too, of the motions of the Heavens, was connected with a vast, an immense system, which joined together a greater number of the most discordant phenomena of nature, than had been united by any other hypothesis; a system in which the principles of connection, though perhaps equally imaginary, were, however, more distinct and determinate, than any that had been known before; and which attempted to trace to the imagination, not only the order of succession by which the heavenly bodies were moved, but that by which they, and almost all other natural objects, had originally been produced.—The Cartesian philosophy begins now to be almost universally rejected, whilst the Copernican system continues to be universally received. Yet it is not easy to imagine, how much probability and coherence this admired system was long supposed to derive from that exploded hypothesis. Till Des Cartes had published his principles, the disjointed and incoherent system of Tycho Brahe, though it was embraced heartily and completely by scarce any body, was yet constantly talked of by all the learned, as, in point of probability, upon a level with Copernicus. They took notice, indeed, of its inferiority with regard to coherence and connection, expressing hopes, however, that these defects might be remedied by some future improvements. But when the world beheld that complete, and almost perfect coherence, which the philosophy of Des Cartes bestowed upon the system of Copernicus, the imaginations of mankind could no longer refuse themselves the pleasure of going along with so harmonious an account of things. The system of Tycho Brahe was every day less and less talked of, till at last it was forgotten altogether.

The system of Des Cartes, however, though it connected together the real motions of the heavenly bodies according to the system of Copernicus, more happily than had been done before, did so only when they were considered in the gross; but did not apply to them, when they were regarded in the detail. Des Cartes, as was said before, had never himself observed the Heavens with any particular application. Though he was not ignorant, therefore, of any of the observations which had been made before his time, he seems to have paid them no great degree of attention; which, probably, proceeded from his own inexperience in the study of Astronomy. So far, therefore, from accommodating his system to all the minute irregularities, which Kepler had ascertained in the movements of the Planets; or from showing, particularly, how these irregularities, and no other, should arise from it, he contented himself with observing, that perfect uniformity could not be expected in their motions, from the nature of the causes which produced them; that certain irregularities might take place in them, for a great number of successive revolutions, and afterwards gave way to others of a different kind: a remark which, happily, relieved him from the necessity of applying his system to the observations of Kepler, and the other Astronomers.

But when the observations of Cassini had established the authority of those laws, which Kepler had first discovered in the system, the philosophy of Des Cartes, which could afford no reason why such particular laws should be observed, might continue to amuse the learned in other sciences, but could no longer satisfy those that were skilled in Astronomy. Sir Isaac Newton first attempted to give a physical account of the motions of the Planets, which should accommodate itself to all the constant irregularities which astronomers had ever observed in their motions. The physical connection, by which Des Cartes had endeavoured to bind together the movements of the Planets, was the laws of impulse; of all the orders of succession, those which are most familiar to the imagination; as they all flow from the inertness of matter. After this quality, there is no other with which we are so well acquainted as that of gravity. We never act upon matter, but we have occasion to observe it. The superior genius and sagacity of Sir Isaac Newton, therefore, made the most happy, and, we may now say, the greatest and most admirable improvement that was ever made in philosophy, when he discovered, that he could join together the movements of the Planets by so familiar a principle of connection, which completely removed all the difficulties the imagination had hitherto felt in attending to them. He demonstrated, that, if the Planets were supposed to gravitate towards the Sun, and to one another, and at the same time to have had a projecting force originally impressed upon them, the primary ones might all describe ellipses in one of the foci of which that great luminary was placed; and the secondary ones might describe figures of the same kind round their respective primaries, without being disturbed by the continual motion of the centres of their revolutions. That if the force, which retained each of them in their orbits, was like that of gravity, and directed towards the Sun, they would, each of them, describe equal areas in equal times. That if this attractive power of the Sun, like all other qualities which are diffused in rays from a centre, diminished in the same proportion as the squares of the distances increased, their motions would be swiftest when nearest the Sun, and slowest when farthest off from him, in the same proportion in which, by observation, they are discovered to be; and that upon the same supposition, of this gradual diminution of their respective gravities, their periodic times would bear the same proportion to their distances, which Kepler and Cassini had established betwixt them. Having thus shown, that gravity might be the connecting principle which joined together the movements of the Planets, he endeavoured next to prove that it really was so. Experience shows us, what is the power of gravity near the surface of the Earth. That it is such as to make a body fall, in the first second of its descent, through about fifteen Parisian feet. The Moon is about sixty semidiameters of the Earth distant from its surface. If gravity, therefore, was supposed to diminish, as the squares of the distance increase, a body, at the Moon, would fall towards the Earth in a minute; that is, in sixty seconds, through the same space, which it falls near its surface in one second. But the arch which the Moon describes in a minute, falls, by observation, about fifteen Parisian feet below the tangent drawn at the beginning of it. So far, therefore, the Moon may be conceived as constantly falling towards the Earth.

The system of Sir Isaac Newton corresponded to many other irregularities which Astronomers had observed in the Heavens. It assigned a reason, why the centres of the revolutions of the Planets were not precisely in the centre of the Sun, but in the common centre of gravity of the Sun and the Planets. From the mutual attraction of the Planets, it gave a reason for some other irregularities in their motions; irregularities, which are quite sensible in those of Jupiter and Saturn, when those Planets are nearly in conjunction with one another. But of all the irregularities in the Heavens, those of the Moon had hitherto given the greatest perplexity to Astronomers; and the system of Sir Isaac Newton corresponded, if possible, yet more accurately with them than with any of the other Planets. The Moon, when either in conjunction, or in opposition to the Sun, appears furthest from the Earth, and nearest to it when in her quarters. According to the system of that philosopher, when she is in conjunction with the Sun, she is nearer the Sun than the Earth is; consequently, more attracted to him, and, therefore, more separated from the Earth. On the contrary, when in opposition to the Sun, she is further from the Sun than the Earth. The Earth, therefore, is more attracted to the Sun: and consequently, in this case, too, further separated from the Moon. But, on the other hand, when the Moon is in her quarters, the Earth and the Moon, being both at equal distance from the Sun, are equally attracted to him. They would not, upon this account alone, therefore, be brought nearer to one another. As it is not in parallel lines however that they are attracted towards the Sun, but in lines which meet in his centre, they are, thereby, still further approached to one another. Sir Isaac Newton computed the difference of the forces with which the Moon and the Earth ought, in all those different situations, according to his theory, to be impelled towards one another; and found, that the different degrees of their approaches, as they had been observed by Astronomers, corresponded exactly to his computations. As the attraction of the Sun, in the conjunctions and oppositions, diminishes the gravity of the Moon towards the Earth, and, consequently, makes her necessarily extend her orbit, and, therefore, require a longer periodical time to finish it. But, when the Moon and the Earth are in that part of the orbit which is nearest the Sun, this attraction of the Sun will be the greatest; consequently, the gravity of the Moon towards the Earth will there be most diminished; her orbit be most extended; and her periodic time be, therefore, the longest. This is, also, agreeable to experience, and in the very same proportion, in which, by computation, from these principles, it might be expected.

The orbit of the Moon is not precisely in the same Plane with that of the Earth; but makes a very small angle with it. The points of intersection with those two Planes, are called, the Nodes of the Moon. These Nodes of the Moon are in continual motion, and in eighteen or nineteen years, revolve backwards, from east to west, through all the different points of the Ecliptic. For the Moon, after having finished her periodical revolution, generally intersects the orbit of the Earth somewhat behind the point where she had intersected it before. But, though the motion of the Nodes is thus generally retrograde, it is not always so, but is sometimes direct, and sometimes they appear even stationary; the Moon generally intersects the Plane of the Earth’s orbit behind the point where she had intersected it in her former revolution; but she sometimes intersects it before that point, and sometimes in the very same point. It is the situation of those Nodes which determines the times of Eclipses, and their motions had, upon this account, at all times, been particularly attended to by Astronomers. Nothing, however, had perplexed them more, than to account for these so inconsistent motions, and, at the same time, preserve their so much sought-for regularity in the revolutions of the Moon. For they had no other means of connecting the appearances together than by supposing the motions which produced them, to be, in reality, perfectly regular and equable. The history of Astronomy, therefore, gives an account of a greater number of theories invented for connecting together the motions of the Moon, than for connecting together those of all the other heavenly bodies taken together. The theory of gravity, connected together, in the most accurate manner, by the different actions of the Sun and the Earth, all those irregular motions; and it appears, by calculation, that the time, the quantity, and the duration of those direct and retrograde motions of the Nodes, as well as of their stationary appearances, might be expected to be exactly such, as the observations of Astronomers have determined them.

The same principle, the attraction of the Sun, which thus accounts for the motions of the Nodes, connects, too, another very perplexing irregularity in the appearances of the Moon; the perpetual variation in the inclination of her orbit to that of the Earth.

As the Moon revolves in an ellipse, which has the centre of the Earth in one of its foci, the longer axis of its orbit is called the Line of its Apsides. This line is found, by observation, not to be always directed towards the same points of the Firmament, but to revolve forwards from west to east, so as to pass through all the points of the Ecliptic, and to complete its period in about nine years; another irregularity, which had very much perplexed Astronomers, but which the theory of gravity sufficiently accounted for.

The Earth had hitherto been regarded as perfectly globular, probably for the same reason which had made men imagine, that the orbits of the Planets must necessarily be perfectly circular. But Sir Isaac Newton, from mechanical principles, concluded, that, as the parts of the Earth must be more agitated by her diurnal revolution at the Equator, than at the Poles, they must necessarily be somewhat elevated at the first, and flattened at the second. The observation, that the oscillations of pendulums were slower at the Equator than at the Poles, seeming to demonstrate, that gravity was stronger at the Poles, and weaker at the Equator, proved, he thought, that the Equator was further from the centre than the Poles. All the measures, however, which had hitherto been made of the Earth, seemed to show the contrary, that it was drawn out towards the Poles, and flattened towards the Equator. Newton, however, preferred his mechanical computations to the former measures of Geographers and Astronomers; and in this he was confirmed by the observations of Astronomers on the figure of Jupiter, whose diameter at the Pole seems to be to his diameter at the Equator, as twelve to thirteen; a much greater inequality than could be supposed to take place betwixt the correspondent diameters of the Earth, but which was exactly proportioned to the superior bulk of Jupiter, and the superior rapidity with which he performs his diurnal revolutions. The observations of Astronomers at Lapland and Peru have fully confirmed Sir Isaac’s system, and have not only demonstrated, that the figure of the Earth is, in general, such as he supposed it; but that the proportion of its axis to the diameter of its Equator is almost precisely such as he had computed it. And of all the proofs that have ever been adduced of the diurnal revolution of the Earth, this perhaps is the most solid and most satisfactory.

Hipparchus, by comparing his own observations with those of some former Astronomers, had found that the equinoctial points were not always opposite to the same part of the Heavens, but that they advanced gradually eastward by so slow a motion, as to be scarce sensible in one hundred years, and which would require thirty-six thousand to make a complete revolution of the Equinoxes, and to carry them successively through all the different points of the Ecliptic. More accurate observations discovered that this procession of the Equinoxes was not so slow as Hipparchus had imagined it, and that it required somewhat less than twenty-six thousand years to give them a complete revolution. While the ancient system of Astronomy, which represented the Earth as the immovable centre of the universe, took place, this appearance was necessarily accounted for, by supposing that the Firmament, besides its rapid diurnal revolution round the poles of the Equator, had likewise a slow periodical one round those of the Ecliptic. And when the system of Hipparchus was by the schoolmen united with the solid Spheres of Aristotle, they placed a new crystalline Sphere above the Firmament, in order to join this motion to the rest. In the Copernican system, this appearance had hitherto been connected with the other parts of that hypothesis, by supposing a small revolution in the Earth’s axis from east to west. Sir Isaac Newton connected this motion by the same principle of gravity, by which he had united all the others, and showed, how the elevation of the parts of the Earth at the Equator must, by the attraction of the Sun, produce the same retrograde motion of the Nodes of the Ecliptic, which it produced of the Nodes of the Moon. He computed the quantity of motion which could arise from this action of the Sun, and his calculations here too corresponded with the observations of Astronomers.

Comets have hitherto, of all the appearances in the Heavens, been the least attended to by Astronomers. The rarity and inconstancy of their appearance, seemed to separate them entirely from the constant, regular, and uniform objects in the Heavens, and to make them resemble more the inconstant, transitory, and accidental phenomena of those regions that are in the neighbourhood of the Earth. Aristotle, Eudoxus, Hipparchus, Ptolemy, and Purbach, therefore, had all degraded them below the Moon, and ranked them among the meteors of the upper regions of the air. The observations of Tycho Brahe demonstrated, that they ascended into the celestial regions, and were often higher than Venus or the Sun. Des Cartes, at random, supposed them to be always higher than even the orbit of Saturn; and seems, by the superior elevation he thus bestowed upon them, to have been willing to compensate that unjust degradation which they had suffered for so many ages before. The observations of some later Astronomers demonstrated, that they too revolved about the Sun, and might therefore be parts of the Solar System. Newton accordingly applied his mechanical principle of gravity to explain the motions of these bodies. That they described equal areas in equal times, had been discovered by the observations of some later Astronomers; and Newton endeavoured to show how from this principle, and those observations, the nature and position of their several orbits might be ascertained, and their periodic times determined. His followers have, from his principles, ventured even to predict the returns of several of them, particularly of one which is to make its appearance in 1758.1 We must wait for that time before we can determine, whether his philosophy corresponds as happily to this part of the system as to all the others. In the meantime, however, the ductility of this principle, which applied itself so happily to these, the most irregular of all the celestial appearances, and which has introduced such complete coherence into the motions of all the Heavenly Bodies, has served not a little to recommend it to the imaginations of mankind.

But of all the attempts of the Newtonian philosophy, that which would appear to be the most above the reach of human reason and experience, is the attempt to compute the weights and densities of the Sun, and of the several Planets. An attempt, however, which was indispensably necessary to complete the coherence of the Newtonian system. The power of attraction which, according to the theory of gravity, each body possesses, is in proportion to the quantity of matter contained in that body. But the periodic time in which one body, at a given distance, revolves round another that attracts it, is shorter in proportion as this power is greater, and consequently as the quantity of matter in the attracting body. If the densities of Jupiter and Saturn were the same with that of the Earth, the periodic times of their several Satellites would be shorter than by observation they are found to be. Because the quantity of matter, and consequently the attracting power of each of them, would be as the cubes of their diameters. By comparing the bulks of those Planets, and the periodic times of their Satellites, it is found that, upon the hypothesis of gravity, the density of Jupiter must be greater than that of Saturn, and the density of the Earth greater than that of Jupiter. This seems to establish it as a law in the system, that the nearer the several Planets approach to the Sun, the density of their matter is the greater: a constitution of things which seems to be the most advantageous of any that could have been established; as water of the same density with that of our Earth, would freeze under the Equator of Saturn, and boil under that of Mercury.

Such is the system of Sir Isaac Newton, a system whose parts are all more strictly connected together, than those of any other philosophical hypothesis. Allow his principle, the universality of gravity, and that it decreases as the squares of the distance increase, and all the appearances, which he joins together by it, necessarily follow. Neither is their connection merely a general and loose connection, as that of most other systems, in which either these appearances, or some such like appearances, might indifferently have been expected. It is everywhere the most precise and particular that can be imagined, and ascertains the time, the place, the quantity, the duration of each individual phenomenon, to be exactly such as, by observation, they have been determined to be. Neither are the principles of union, which it employs, such as the imagination can find any difficulty in going along with. The gravity of matter is, of all its qualities, after its inertness, that which is most familiar to us. We never act upon it without having occasion to observe this property. The law too, by which it is supposed to diminish as it recedes from its centre, is the same which takes place in all other qualities which are propagated in rays from a centre, in light, and in every thing else of the same kind. It is such, that we not only find that it does take place in all such qualities, but we are necessarily determined to conceive that, from the nature of the thing, it must take place. The opposition which was made in France, and in some other foreign nations, to the prevalence of this system, did not arise from any difficulty which mankind naturally felt in conceiving gravity as an original and primary mover in the constitution of the universe. The Cartesian system, which had prevailed so generally before it, had accustomed mankind to conceive motion as never beginning, but in consequence of impulse, and had connected the descent of heavy bodies, near the surface of the Earth, and the other Planets, by this more general bond of union; and it was the attachment the world had conceived for this account of things, which indisposed them to that of Sir Isaac Newton. His system, however, now prevails over all opposition, and has advanced to the acquisition of the most universal empire that was ever established in philosophy. His principles, it must be acknowledged, have a degree of firmness and solidity that we should in vain look for in any other system. The most sceptical cannot avoid feeling this. They not only connect together most perfectly all the phenomena of the Heavens, which had been observed before his time; but those also which the persevering industry and more perfect instruments of later Astronomers have made known to us have been either easily and immediately explained by the application of his principles, or have been explained in consequence of more laborious and accurate calculations from these principles, than had been instituted before. And even we, while we have been endeavouring to represent all philosophical systems as mere inventions of the imagination, to connect together the otherwise disjointed and discordant phenomena of Nature, have insensibly been drawn in, to make use of language expressing the connecting principles of this one, as if they were the real chains which Nature makes use of to bind together her several operations. Can we wonder then, that it should have gained the general and complete approbation of mankind, and that it should now be considered, not as an attempt to connect in the imagination the phenomena of the Heavens, but as the greatest discovery that ever was made by man, the discovery of an immense chain of the most important and sublime truths, all closely connected together, by one capital fact, of the reality of which we have daily experience.

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Note by the Editors.

The Author, at the end of this Essay, left some Notes and Memorandums, from which it appears, that he considered this last part of his History of Astronomy as imperfect, and needing several additions. The Editors, however, chose rather to publish than suppress it. It must be viewed, not as a History or Account of Sir Isaac Newton’s Astronomy, but chiefly as an additional illustration of those Principles in the Human Mind which Mr. Smith has pointed out to be the universal motives of Philosophical Researches.

THE PRINCIPLES

WHICH LEAD AND DIRECT